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# Title: LBr. 57, 2 · Bernoulli, Joh.
# Folio 197r, page id DE-611-HS-3653099:0393
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Ecce interium quam petis demonstrationem
s
meam illius egeorematis per quam carisim
videbis, corus aliquod ex g. 2 gradinis velolitatis
motum, posse effectum praestare quadruplo majore
isn
quam corpus idem vel aequale unocum velolitatis
2
ver. L3.
X
lec
2
in
2
p
facipe anim Corpus C moveri oblique in Elastium L ne loci
tate CL, ut 2 jangulo inclinationis eL p existente 30. grad
7a
Cajus nempe sinus Cp est semissis radii (L, supponio aute
le l
am esse resistentiam in rlassio ut ad illud tendendendum
requilatur praetise unus veloeitatis gradus in ilo cor
pore, si perpendiculariter impingeret. Quid ergo jam fiet
1
post concursionem obliquam corporis i elasttum L
voniam motus per CL componitur ut notum est ex
duobus collateralibus per CB et PL, et cum Cp. secur
dum quam corpus directe impingit in Elastrum exsio
mal dimidiam velocitatem corporis per L, consumetur
hic motus per (s, tento etastio, Merinde enim esset
ac si corpus cellritate ep perpendiculariter incursero
in dastrum, quod per Hypothesin illaq celeritotem
a Lemanent ecorporis celeritate et directi
ne
 DL. producta anitur, L in M, ita ut LM sit  BL 
.l
coruere potest
L13 (poritur enim es - 2) et applicate in I alio
e
d
Simili elastro faciente cum LM angulum LMZ cujus sinuc 19
= Cp = 1 per eandem rationem manifectum est corpus C post
tensionem Elastri L, tensurum esse Elastium M, umasso
motu per L4 et servato motu per qm; proloneala itaque yM
ad M ut fiat  MN = QM = 12 obique substituto elastio
simili tertio constituente cum MN angulum MNR semirectum
quo scilicet ne iterum sit Cp=1 patet similiter notum per MR. toturi
empendi in ponsiomem plastrix, corpore interim movers pergente directione
11